June 2024 Paper 3 Q3
3. Ming is studying the large data set for Perth in 2015
He intended to use all the data available to find summary statistics for the Daily Mean Air Temperature, \(x\) °C.
Unfortunately, Ming selected an incorrect variable on the spreadsheet.
This incorrect variable gave a mean of 5.3 and a standard deviation of 12.4
The correct values for the Daily Mean Air Temperature are summarised as
\[n = 184 \qquad \sum x = 2801.2 \qquad \sum x^2 = 44\,695.4\]One of the months from the large data set for Perth in 2015 has
- mean \(\bar{x} = 19.4\)
- standard deviation \(\sigma_x = 2.83\)
for Daily Mean Air Temperature.
| Scheme | Marks | AO |
|---|---|---|
| Rain[fall] (allow [Mean] Windspeed) | B1 | 1.2 |
| (1) |
Notes
Answers may appear next to the question.
B1 for Rain[fall] or precipitation (e.g. allow Daily Total [or Mean or max] Rainfall etc)
(or allow Mean Windspeed or just “windspeed” BUT not max windspeed or “gust”)
If they give more than one answer we take the last one.
(NB Actual windspeed mean is 8.2, sd 2.38. No other quantitative variables available)
| Scheme | Marks | AO |
|---|---|---|
| [\(\bar{x} =\)] \(15.2239\ldots =\) awrt 15.2 | B1 | 1.1b |
| \(\sigma_x = \sqrt{\dfrac{44\,695.4}{184} - \text{``}15.22..\text{''}^2}\) or \(\sqrt{11.1(422\ldots)}\) | M1 | 1.1b |
| \(= 3.33800\ldots\) awrt 3.34 | A1 | 1.1b |
| (3) |
Notes
B1 for awrt 15.2 (Do not accept fractions or mixed numbers)
M1 for a correct expression including square root (ft their mean)
May be implied by an answer of 3.3 or better.
A1 for awrt 3.34
[Allow \(s = 3.3471\ldots\) i.e. awrt 3.35 if correct formula/expression is seen]
| Scheme | Marks | AO |
|---|---|---|
| Mean is higher than average OR a summer/spring month If they say winter/autumn they must explain that these are hotter months for Perth. | M1 | 2.4 |
| [Perth is southern hemisphere or Australia so latest available] month is Oct | A1cso | 2.2b |
| (2) | ||
| (6 marks) |
Notes
If answer in (b)(i) \(\gt 19.4\) and an attempt is made in (c) please send to review.
M1 for a reason mentioning that mean or temperature is higher (o.e.)
e.g. it is a warmer/hotter month is OK
or sight of \(19.4 \gt\) (their) 15.2
Only ft their 15.2 if it is less than 19.4
OR suggesting a summer/spring month.
Ignore incorrect statements that are irrelevant or don’t contradict
For incorrect statements that contradict score M0
A1cso dep on M1 scored for inferring October
Must choose just October not a range like August~October
(NB actual mean for Sep is 15.6 and sd 3.19 and this scores A0)
Can accept for example “high mean so December” for M1A0
SC M1A1 for “October since Perth is in the southern hemisphere/Australia”
M1A0 for “Sep or Nov or Dec or Jan or Feb and “Perth is in the southern hemisphere/Australia”
M0A0 just “Perth is in the southern hemisphere/Australia” without a month M0A0